Question: Solve for $x$ and $y$ using elimination. ${-3x-2y = -31}$ ${3x+5y = 46}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the top and bottom equations together. $3y = 15$ $\dfrac{3y}{{3}} = \dfrac{15}{{3}}$ ${y = 5}$ Now that you know ${y = 5}$ , plug it back into $\thinspace {-3x-2y = -31}\thinspace$ to find $x$ ${-3x - 2}{(5)}{= -31}$ $-3x-10 = -31$ $-3x-10{+10} = -31{+10}$ $-3x = -21$ $\dfrac{-3x}{{-3}} = \dfrac{-21}{{-3}}$ ${x = 7}$ You can also plug ${y = 5}$ into $\thinspace {3x+5y = 46}\thinspace$ and get the same answer for $x$ : ${3x + 5}{(5)}{= 46}$ ${x = 7}$